Almost every convex or quadratic programming problem is well posed

• 成果类型: Article
• 署名作者: Ioffe, AD; Lucchetti, RE; Revalski, JP
• 署名单位: Technion Israel Institute of Technology; Polytechnic University of Milan; Bulgarian Academy of Sciences
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1030.0080
• 发表日期: 2004
• 页码: 369-382
• 关键词: banach-mazur game; optimization problems; calculus

摘要

We provide an abstract principle aimed at proving that classes of optimization problems are typically well posed in the sense that the collection of ill-posed problems within each class is sigma-porous. As a consequence, we establish typical well-posedness in the above sense for unconstrained minimization of certain classes of functions (e.g., convex and quasi-convex continuous), as well as of convex programming with inequality constraints. We conclude the paper by showing that the collection of consistent ill-posed problems of quadratic programming of any fixed size has Lebesgue measure zero in the corresponding Euclidean space.